Self-Consistent Description of Interacting Phonons in a Crystal Lattice

  • Yu. M. Poluektov National Science Center “Kharkov Institute of Physics and Technology” 1, Akademicheskaya Str., 61108 Kharkov, UkraineKharkоv V.N. Karazin National UniversitySq. Svobody 4, Kharkov, 61022, Ukraine https://orcid.org/0000-0002-3207-3226
Keywords: phonon, specific heat, phonon- phonon interaction, Debye energy, quasiparticle

Abstract

Self-consistent approach for interacting phonons description in lattice, which generalizes Debye model, is proposed. Notion of “selfconsistent” phonons is introduced, speed of which depends on temperature and is determined from non-linear equation. Debye energy is also a function of temperature in this approach. Thermodynamics of “self-consistent” phonon gas is constructed. It is shown, that at low temperatures there is a correction propotional to the seventh power of temperature to the cubic law of specific heat dependence on temperature. This may be one of the reasons why cubic law for specific heat is observed only at rather low temperatures. At high temperatures the theory predicts linear deviation from Dulong-Petit law, which is observed experimentally.

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Author Biography

Yu. M. Poluektov, National Science Center “Kharkov Institute of Physics and Technology” 1, Akademicheskaya Str., 61108 Kharkov, UkraineKharkоv V.N. Karazin National UniversitySq. Svobody 4, Kharkov, 61022, Ukraine

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Published
2016-12-14
Cited
How to Cite
Poluektov, Y. M. (2016). Self-Consistent Description of Interacting Phonons in a Crystal Lattice. East European Journal of Physics, 3(3), 35-46. https://doi.org/10.26565/2312-4334-2016-3-03